For someone who has "nil" knowledge of Latin grammar, I'm really impressed with your attempt: there's only one grammatical error and the meaning is fairly clear.
First, a grammar correction: internexus is presumably a neologism derived from nexus, which is the 4th declension. You will thus want to use the ablative singular form:
In internexu potes esse canis.
Literally, this translates as: "On the internet, you can be a dog." As @Rafael pointed out in his comment, this "can" refers to ability, not permission as can be the case in English. As it stands this is a reasonable attempt at translation, though I tend to think that the joke gets obscured ("you can be a dog...even though everyone thinks you're a human").
@SamK's translation is literal but perfectly good. I would just amend to the more commonly understood calque interrete:
In interrete, nemo scit te canem esse.
My proposed translation would rework this a little bit to a more idiomatic phrasing:
In interrete, canis et homo non distant.
On the internet, a dog and a man do not differ. (lit. "are not distant")
In interrete, canis ab homine haud differt.
On the internet, a dog is not different from a man.
or slightly more elliptical:
In interrete, canis non cognoscitur.
On the internet, a dog is not recognized.
I like the two last (bolded) suggestions best.